4.32. Consider a production system consisting of a machine center followed by an

inspection station. Arrivals from outside the system occur only at the machine center

and follow a Poisson process with rate . The machine center and inspection station

are each single server operations with rates 1 and 2. Suppose that each item

independently passes inspection with probability p. When an object fails inspection

it is sent to the machine center for reworking. Find the conditions on the parameters

that are necessary for the system to have a stationary distribution.